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Financial Maths, STD1 F1 2021 HSC 19

Yin purchased a car for $20 000. The value of the car decreases according to a linear model. The graph shows the value of the car,  $\(V\), against the time,  \(t\) months, since it was purchased.
 


 

  1. By how much does the value of the car decrease every 10 months?   (1 mark)

  2. Find the value of the car after 5 years.   (1 mark)

  3. Identify ONE problem with using this model to determine the value of Yin’s car over time.   (1 mark)

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a.    \($2000\)

b.    \($8000\)

c.    \(\text{Car will have a negative value after 100 months.}\)

Show Worked Solution

a.    \(\text{Decrease (10 months)}= 20\,000-18\,000= $2000\)
  

b.   \(\text{5 years} = 5 \times 12 = 60\ \text{months}\)

\(\text{At}\ \ t=60\ \text{(from graph)}:\)

\(V = $8000\)

c.   \(\text{Car will have a negative value after 100 months.}\)

♦ Mean mark (c) 11%.

Financial Maths, STD2 F1 2021 HSC 19

Adam purchased some office furniture five years ago. It depreciated by $2300 each year based on the straight-line method of depreciation. The salvage value of the furniture is now $7500.

Find the initial value of the office furniture.   (2 marks)

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`$19\ 000`

Show Worked Solution

`text{Find initial value}\ (V_0):`

`S` `=V_0-Dn`  
`7500` `=V_0-2300 xx 5`  
`V_0` `=7500 + 11\ 500`  
  `=$19\ 000`  

Financial Maths, STD2 F1 EQ-Bank 19

Michelle intends to keep a car purchased for $17 000 for 15 years. At the end of this time its value will be $3500.

  1. By what amount, in dollars, would the car’s value depreciate annually if Michelle used the flat rate method of depreciation?   (1 mark)

  2. Determine the annual flat rate of depreciation correct to one decimal place.   (1 mark) 

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a.    `$900`

b.    `5.3text{%  (1 d.p.)}`

Show Worked Solution

a.    `text(Depreciation)= 17\ 000-3500= $13\ 500`

`:.\ text(Annual depreciation)= (13\ 500)/15= $900`
  

b.    `:.\ text(Flat rate of depreciation )`

`= 900/(17\ 000) xx 100text(%)`

`= 5.29 …= 5.3text{%  (1 d.p.)}`

Financial Maths, STD2 F1 EQ-Bank 18

Khan paid $900 for a printer.

This price includes 10% GST (goods and services tax).

  1. Determine the price of the printer before GST was added.

     

    Write your answer correct to the nearest cent.   (2 marks)

  2. Khan is able to depreciate the full $900 purchase price of his printer for taxation purposes.

     

    Under flat rate depreciation the printer will be valued at $300 after five years.

     

    Calculate the annual depreciation in dollars.   (1 mark)

Show Answers Only

a.    `$818.18`

b.    `$120`

Show Worked Solution

a.    `text(Let)\ \ $P = text(price ex-GST)`

COMMENT: Reverse GST questions regularly cause problems for many students.
`:. P + 10text(%) xx P` `= 900`
`1.1P` `= 900`
`P` `= 900/1.1`
  `= 818.181…`
  `= $818.18\ \ text(nearest cent)`

 

b.    `text(Annual depreciation)= ((900-300))/5= $120`

Financial Maths, STD2 F1 EQ-Bank 17

A company purchased a machine for $60 000.

For taxation purposes the machine is depreciated over time using the straight line depreciation method.

The machine is depreciated at a flat rate of 10% of the purchase price each year.

  1. By how many dollars will the machine depreciate annually?   (1 mark)

  2. Calculate the value of the machine after three years.   (1 mark)

  3. After how many years will the machine be $12 000 in value?   (1 mark)

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a.    `$6000`

b.    `$42\ 000`

c.    `8\ text(years)`

Show Worked Solution

a.    `text(Annual depreciation)= 10text(%) xx 60\ 000= $6000`
   

b.    `text(After 3 years,)`

`text(Value)` `=V_0-Dn`
  `= 60\ 000-(3 xx 6000)`
  `= $42\ 000`

 

c.    `text(Find)\ n\ text(when value = $12 000)`

`12\ 000` `= 60\ 000-6000 xx n`
`6000n` `= 48\ 000`
`:.n` `=(48\ 000)/6000`
  `= 8\ text(years)`

Financial Maths, STD2 F1 EQ-Bank 16

Hugo is a professional bike rider.

The value of his bike will be depreciated over time using the flat rate method of depreciation.

The graph below shows his bike’s initial purchase price and its value at the end of each year for a period of three years.
 

  1. What was the initial purchase price of the bike?   (1 mark)

  2. Use calculations to show that the bike depreciates in value by $1500 each year.   (1 mark)

  3. Assume that the bike’s value continues to depreciate by $1500 each year. Determine its value five years after it was purchased.   (1 mark)

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a.    `$8000`

b.    `text(See Worked Solutions)`

c.    `$500`

Show Worked Solution

a.    `$8000`
 

b.    `text(Value after 1 year) = $6500\ \ \ text{(from graph)}`

`:.\ text(Annual depreciation)= 8000-6500= $1500`

c.    `text(After 5 years:)`

`S` `=V_0-Dn`
  `=8000-5 xx 1500`
  `=$500`

Financial Maths, STD2 F1 EQ-Bank 3 MC

Rae paid  $40 000  for new office equipment at the start of the 2013 financial year.

At the start of each following financial year, she used flat rate depreciation to revalue her equipment.

At the start of the 2016 financial year she revalued her equipment at  $22 000.

The annual flat rate of depreciation she used, as a percentage of the purchase price, was

  1. 11.25%
  2. 15%
  3. 17.5%
  4. 35%
Show Answers Only

`B`

Show Worked Solution

`text(Depreciation over 3 years)`

♦ Mean mark 50%.

`=40\ 000-22\ 000=$18\ 000`

`:.\ text(Annual depreciation) = (18\ 000)/3 = $6000`

`:.\ text(Depreciation rate) = 6000/(40\ 000) = 0.15 = 15text(%)`

`=> B`

Financial Maths, STD2 F1 2017 HSC 11 MC

A new car was bought for $19 900 and one year later its value had depreciated to $16 300.

What is the approximate depreciation, expressed as a percentage of the purchase price?

  1. 18%
  2. 22%
  3. 78%
  4. 82%
Show Answers Only

`A`

Show Worked Solution

`text(Net Depreciation)= 19\ 900-16\ 300= $3600`

`:. %\ text(Depreciation)= 3600/(19\ 900) xx 100= 18.09…text(%)`
  

`=>A`

Financial Maths, STD2 F1 2007 HSC 26b

Myles is in his third year as an apprentice film editor.

  1. Myles purchased film-editing equipment for $5000.

     

    After 3 years it has depreciated to $3635 using the straight-line method.  

     

    Calculate the rate of depreciation per year as a percentage.   (2 marks)

  2. Myles earns $800 per week. Calculate his taxable income for this year if the only allowable deduction is the amount of depreciation of his film-editing equipment in the third year of use.   (1 mark)

  3. Use this tax table to calculate Myles’s tax payable.   (2 marks)
     
          

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a.   `text(9.1%)`

b.   `$41\ 145`

c.   `$8443.50`

Show Worked Solution
a.    `S = V_0-Dn`
  `S = $3635,\ \ \ V_0 = 5000,\ \ \ n = 3`
`3635` `= 5000-D xx 3`
`3D` `= 1365`
`D` `= $455`

 

`:.\ text(Rate of depreciation per year)`

`= 455/5000 xx 100`

`= 9.1 text(%)`

b.    `text(Income per year)= 52 xx 800= $41\ 600`

`text(Taxable income)` `=\ text(Income – Deductions)`
  `= 41\ 600-455= $41\ 145`

 

c.    `text(Tax payable)` `= 4500 + 0.3(41\ 145-28\ 000)`
    `= 4500 + 3943.50= $8443.50`

Financial Maths, STD2 F1 2010 HSC 11 MC

Which of the following graphs shows the lowest rate of depreciation over the given time period?
 

Capture4

Capture5

Show Answers Only

`D`

Show Worked Solution

`text(The lowest rate of depreciation will occur when)`

`text(an item retains value for the longest time.)`

`=>  D`